Let us notice that for the memory term we have obtained a different result for the equation of motions from the one that we would have obtained working in In-Out formalism. This result agrees with \(S_2 \)  in Eq.(203) given in [1]}. Notice that in [1]} the authors are using a different parametrization of the \(\pm \)  variables with respect to ours. For this reason we should multiply Eq.(203) by an overall factor \(\sqrt{2}/2\)  in order to compare it to our result.
